# What is the stiffness for a far end fixed beam?

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What is the stiffness for a far end fixed beam?
1. $K=\dfrac{3EI}{L}$
2. $K=\dfrac{4EI}{L}$
3. $K=\dfrac{12EI}{L}$
4. $K=\dfrac{16EI}{L}$
5. $K=\dfrac{20EI}{L}$

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Correct Answer - Option 2 : $K=\dfrac{4EI}{L}$

Explanation

Stiffness (k) is defined as the force per unit deflection or moment required per unit rotation.

Stiffness factor for a beam simply supported at both ends is 3EI/L

Important Points:

For the far end being Hinged Supported:

If a unit rotation is to be caused at an end A for the far end being hinged support. Moment of $\frac{{3EI}}{L}$ is to be applied at end and hence stiffness for the member is said to be $\frac{{3EI}}{L}.$

For the far end being Fixed Supported:

If a unit rotation is to be caused at an end A for the far end being fixed supported. Moment of $\frac{{4EI}}{L}$ is to be applied at end and hence stiffness for the member is said to be $\frac{{4EI}}{L}.$